What can I check with my ohm meter?
You can check about anything with one. Just make sure you have some spare fuses for it in case it says you shouldn't have checked that.
I did have to think about this for a bit. I am used to talking service techs through something like this I guess I do have to worry about liability a little.
So here goes your crash course in low voltage HVAC.
When you say you swapped tsat's I'm guessing you have the ones that just snap off with some pins coming out the back to contact the backplate.
Pull the tsat off the the running unit. From your description it should stay running. If it stops your problem may be in the backplate or the wires to the backplate.
If it keeps running, go find your service switch or breaker to turn it off. Pull the backplate off the wall and check for broken or bare wires touching each other. As soon as you pull it off they stop touching so this may be hard to see.
If you don't find a problem there then you need to ohm between the wires. I have seen a lot of different color wires used on the low voltage side so I have to do more guessing that this is a standard red, white, green and yellow single transformer system.
With the power still off, go to the unit and find the red transformer wire and the green fan wire. I will say again that you may not have these colors. Unhook the two wires and ohm between them. It should be open. If you are reading the wires as closed you have a short in the wires somewhere between the unit and tsat.
If all of this checks good then you may have a relay problem. I would like to see how it is wired before I go to far into telling you what to check on that
jim
Just read your post as I was posting this. Get a wiring diagram so we can tell you how to check that fan relay.